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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Grand Unification: A Single-Axiom Derivation of 100 Physical Observables from Maximum Entropy Production

Authors: capron, mathias;

The Grand Unification: A Single-Axiom Derivation of 100 Physical Observables from Maximum Entropy Production

Abstract

We derive the totality of known fundamental physics from a single axiom: Maximum Entropy Production (MEP). No geometric input is assumed. No physical constant is fitted. The theory contains zero adjustable parameters. Via Perelman's entropy-monotonic Ricci flow, MEP uniquely selects the round three-sphere S³ (isomorphic to SU(2)) as the spatial micro-geometry. The topological action S_cell = π²/2 is derived from MaxCal dynamics on S³, generating the universal Boltzmann weight α₀ = exp(−π²/2) ≈ 7.19 × 10⁻³. The Standard Model gauge group SU(3)c × SU(2)L × U(1)Y emerges from Hurwitz–Cartan octonion completion. Three fermion generations follow from the Adams theorem on S³. The framework produces 100 Level-0 predictions spanning 60 orders of magnitude, including: — The fine-structure constant: α⁻¹ = exp(π²/2) − 2 + 1/55 = 137.064 (0.02% deviation) — All nine fermion masses from a single formula mf = cf × M★ × α₀^qf, with exponents and prefactors derived from the Dirac spectrum on S³ — The full CKM and PMNS mixing matrices (14/14 parameters from Haar measure and polyhedral holonomy) — The cosmological constant: λΛ = α₀⁵⁶ / (2√3 π²) ≈ 2.81 × 10⁻¹²² (1.1% deviation) — The Hubble tension ratio: H_local / H_CMB = 1 + √α₀ ≈ 1.085 (0.05% deviation) — The dark-to-baryonic matter ratio: Ωc/Ωb = 65/12 = 5.417 (1.1% deviation) — The proton mass, neutron–proton mass splitting, Higgs mass, Weinberg angle, and 80+ additional observables Performance: median deviation 0.88% across 38 continuous observables, with 89% falling below 3% and 50% below 1%. The number π is not a mathematical convenience but the unique self-consistent fixed point of the theory, closing the cycle MEP → Perelman → S³ → π²/2 → α₀ → Standard Model through the gravitational identity π⁶ = 960 × exp₃(η) (verified to 0.4 ppm). Seven epistemological stress-tests are addressed with full mathematical proofs (Appendices H–O), covering: the status of the mass anchor M★, the spectral anatomy of α⁻¹, the cosmological coincidence problem, Lorentzian time emergence via Osterwalder–Schrader reconstruction, renormalization scale anchoring, the Lichnerowicz obstruction for neutrinos, and the gravitational self-consistency loop. An additional appendix (P) resolves the black hole information paradox within the framework, predicting a negative linear quantum correction to Bekenstein–Hawking entropy — unique among all quantum-gravity approaches. The paper lists 20 near-term falsifiable wagers testable by DUNE, JUNO, LiteBIRD, CMB-S4, DESI, Euclid, and HL-LHC between 2026 and 2035. Zero free parameters means a single significant discrepancy kills the entire framework.

Keywords

Keywords: maximum entropy production, Ricci flow, Perelman entropy, three-sphere, Standard Model, gauge unification, fermion masses, mixing matrices, cosmological constant, Hubble tension, zero free parameters, falsifiable predictions, Maximum Entropy Production, S³ Topology, Fine-Structure Constant, Fermion Masses, CKM Matrix, Weinberg Angle, Neutrino Mixing, CP Violation, Hubble Tension, KSS Bound, Fundamental Constants, Geometric Physics, Quantum Mechanics, Standard Model

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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